Mathematical modelling of solute transport in a heterogeneous aquifer
This study provides a contribution to the understanding of parsimony and predictive uncertainty in the context of groundwater solute transport modelling. The study is unique because the modelling was undertaken using tracer test data from a heterogeneous artificial aquifer whose structure was known to a very high level of detail. The aquifer structure was based on a ‘real life’ Canterbury Plains alluvial aquifer (in New Zealand). Parsimonious principles were applied by starting with a simple analytical model that assumed homogeneity then progressively adding heterogeneity using numerical models with varying degrees of parameterisation complexity. The results show that increased complexity did not necessarily make the model better at replicating the tracer test data. For example, the outputs from a numerical model that represented heterogeneity using a zone based approach based on the recorded distribution of all 2,907 blocks that comprised the artificial aquifer was little different to a simple numerical model that adopted a homogenous distribution and included a single value of dispersion. Parameterisation of numerical models using ‘pilot points’ provided the most complex representation of heterogeneity and resulted in the best replication of the tracer test data. However, increasing model complexity had its disadvantages such as decreasing parameterisation uniqueness. The contribution to predictive uncertainty from model parameters and observations was assessed using a linear approach based on Bayes theorem. This approach has been applied to other groundwater modelling studies, but not to solute transport modelling within Canterbury Plains alluvial aquifers or to an artificial aquifer. A unique finding was the reduction in predictive uncertainty along the groundwater flow path. This finding correlated well with the numerical model outputs which showed closer fits to the observation data near the end of the aquifer compared to those near the top of the aquifer where the tracer was injected. Physical solute transport processes were identified and described as part of the modelling. These included the increase in dispersivity with travel distance and the spatial distribution of the aquifer hydraulic properties. Analytical modelling was a useful tool in identifying physical processes, aquifer characteristics and the variation in aquifer hydraulic properties both spatially and with depth. An important finding was the value of undertaking multiple modelling approaches. This is because each approach has its own advantages and disadvantageous and by comparing the results of different approaches, the true facts about the aquifer system are made clearer.